C₁₁×#11912 #14589105

order	2816
nilpotency class	4
isoclinism	isoclinic class of #11912
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#11912

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1530
commutator	C₄²	C₂²×C₄×C₁₁
Frattini, cosocle	#97	C₂³×C₁₁
prime radical	C₁₁×#540	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₁₁×#405 ◁ G

284 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 352

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,21,16,18,30,32,17,22,29,38,31,20,27,37)(14,23,25,40,26,35,42,39,24,36,28,43,41,19,33,34);(13,18)(15,27)(16,31)(19,23)(20,22)(21,38)(25,33)(26,41)(28,42)(29,30)(34,39)(35,36);(12,14)(13,19,22,35)(15,28)(16,26)(17,24)(18,23,20,36)(21,39,38,34)(25,29)(27,42)(30,33)(31,41)(32,43,37,40)

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 4900);